Minimal functional bases for elasticity tensor symmetry classes

Abstract

Functional bases, synonymous with separating sets, are usually formulated for an entire vector space, such as the space Ela of elasticity tensors. We propose here to define functional bases limited to symmetry strata, i.e. sets of tensors of the same symmetry class. We provide such lowcardinal minimal bases for tetragonal, trigonal, cubic or transversely isotropic symmetry strata of the elasticity tensor.

arXiv commentJournal of Elasticity, Springer Verlag, 2022

References in corpus (4)

• A minimal integrity basis for the elasticity tensor
• Harmonic factorization and reconstruction of the elasticity tensor
• Generic separating sets for 3D elasticity tensors
• A Polynomially Irreducible Functional Basis of Elasticity Tensors

Cited by in corpus (3)

• Cauchy relations in linear elasticity: Algebraic and physics aspects
• Construction of minimal integrity basis for anisotropic hyperelasticity via structural tensors
• Upper bounds estimates of the distance to cubic or orthotropic elasticity